The Experts Strike Back

A Critical Appraisal of the Matching Law Article

After publishing the previous article on the matching law, an idea struck me—why not reach out to the experts? You know, the folks who actually worked extensively on the matching law and are privy to its theoretical nuances and conceptual underpinnings. What did my article get right/wrong? Would they find my lack of understanding disturbing? What additional insights should I (and you) be cognizant of?

First, for those who have yet to read the matching law article, here it is:

Only a Sith Deals in Absolutes

And now, the experts.

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William M. Baum

Billy Baum was a key early contributor to matching theory, and his 1974 article on the generalised matching law has been cited over 2,000 times¹.

Here are excerpts from our exchange, reproduced with his permission (bolding mine):

Thank you for sending the article. It makes the basic concepts clear, particularly as to application. Relative measures are key. My research has gone far beyond the original 1961 law. I particularly avoid the term "value", because it invokes folk psychology, with its notions about free will and autonomy.

When asked how we should characterise what drives matching without reference to “value”, Baum responded

The way I think about the matching law is that the more general relation is the Law of Allocation (aka the generalized matching law), which states that activities of an organism compete with one another for time according to their competitive weight, which depends upon induction—the degree to which an activity is induced by environmental events, particularly those with evolutionary significance and their proxies. Operant activities are induced by their consequences.

It appeared to me “competitive weight” and “value” were merely describing the same mechanism in different words. I prodded further, to which Baum replied

I avoid "value" because of its mentalistic connotations. Competitive weight fits with the idea that activities compete for time, and competitive weight depends on induction. In fact, it forms the basis for a mathematical formulation [shared in the paper linked below].

As Baum explains, activities compete for our time (and attention and effort). The competitive weight of each activity determines if an activity can “win” a share of our time, and if so, by how much. He calls this the Law of Allocation.

This competitive weight is driven by environmental events of evolutionary significance and their proxies (Law of Induction). These events induce the relative rates of activity.

These two Laws, alongside a third Law of Covariance are laid out in this article, kindly shared by Baum.

2026 Behavior Process And Evolution In Mmv

886KB ∙ PDF file

Download

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You can also read Baum’s book Introduction to Behavior: An Evolutionary Perspective for a deeper foray. Finally, here’s a video for those who prefer audio-visual information:

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John E. R. Staddon

John Staddon was another key early contributor to the matching law, being the first to propose the aforementioned generalised matching law.

Staddon believed that matching should not be taken at face value. He introduces the idea of maximising, a concept familiar to those trained in economics. Individuals allocate behaviour across activity choices in a way that maximises the overall rate of payoffs.

A further distinction can be made between momentary (or local) maximisation and overall (or global) maximisation. Momentary maximisation can be understood through a hill climbing analogy:

Imagine a blind man trying to get to the top of a mountain. Their decision rule is simple—if the next step forward slopes up, take that step; if it slopes down or is level, try another way.

In other words, always pick the best immediately available option.

In contrast, overall maximisation involves taking into account distal contextual factors, analogous to a hill climber with unimpaired vision who is able to see the the lay of the land and orients towards the peak in the distance, even if the next step forward slopes down. Overall maximisation can produce scenarios such as allocating responses to activities that produce little to no immediate payoff, but a large payoff in the future (delay discounting).

Which strategy do we employ?

As Staddon writes in his book Adaptive Behaviour and Learning (a more recent edition can be found here):

Animals seem to take each choice as it comes and respond according to a relatively simple decision rule, appropriate to the particular situation. But in every well-studied situation, the decision rule seems sensitively attuned to global consequences². Animals do hill-climb, in the sense that they evaluate each choice according to a simple rule that embodies what they know of the probable payoff for each choice. But their rules take into account more than the immediate consequences of a choice.

Essentially, we tend to employ momentary maximisation strategies, but also seem somewhat attuned to the broader context. This leads to a curious bias: we tend to overallocate behaviours (or overmatch) to activities with higher payoffs, and underallocate behaviours (or undermatch) to activities with lower payoffs. As it turns out, this bias tends to improve overall maximisation.

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And that’s it from the experts!

One last thing:

1. I was introduced to Baum’s work through his book Understanding Behaviourism: Behaviour, Culture, and Evolution as a graduate student, which has a profound influence on my worldview. As some long-term readers may know, many of the ideas in this blog extend from Baum’s work.

2. Staddon is careful to note that these findings are derived from non-human studies. Which does not mean they are not relevant.

As he states in his book preface,

“Animals are worth studying because they are intrinsically interesting, relatively easy to experiment on, complicated enough to be a challenge — and not as smart as we are. Perhaps we can actually begin to understand them scientifically in a reasonable time. I firmly believe that if we want to build a scientific understanding of the evolution and meaning of intelligence, in people as well as animals and machines, we must begin with animals — and in study that is directed at the problems they pose, without one eye always on what ails human beings. I am certain that the eventual payoff will indeed be an understanding of people as well as beasts. But solving human behavioral problems is likely to take some time, and it may be impeded by impatience to run before we can walk.”